Problem: Nadia is 4 times as old as Christopher. Six years ago, Nadia was 7 times as old as Christopher. How old is Christopher now?
Explanation: We can use the given information to write down two equations that describe the ages of Nadia and Christopher. Let Nadia's current age be $n$ and Christopher's current age be $c$ The information in the first sentence can be expressed in the following equation: $n = 4c$ Six years ago, Nadia was $n - 6$ years old, and Christopher was $c - 6$ years old. The information in the second sentence can be expressed in the following equation: $n - 6 = 7(c - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $c$ , it might be easiest to use our first equation for $n$ and substitute it into our second equation. Our first equation is: $n = 4c$ . Substituting this into our second equation, we get: $4c$ $-$ $6 = 7(c - 6)$ which combines the information about $c$ from both of our original equations. Simplifying the right side of this equation, we get: $4 c - 6 = 7 c - 42$ Solving for $c$ , we get: $3 c = 36.$ $c = 12$.